\documentclass[border=5mm,12pt]{standalone}

\usepackage{tikz}
\usepackage{ctex}
\usetikzlibrary{calc}
\usetikzlibrary{positioning}

\tikzset{tree/.style={every node/.style={circle, draw}}}

\begin{document}

\begin{tikzpicture}[
        squarenode/.style={draw, rectangle, minimum size=1cm},
    ]
    \node[squarenode] (a) {a};

    \node[squarenode, below left=of a] (p) {p};
    \node[squarenode, below right=of a] (q) {q};

    \draw (a.south) -- (p.north);
    \draw (a.south) -- (q.north);

    \node[below] at (current bounding box.south) {2-node};
\end{tikzpicture}

\end{document}
